Number worksheet — GCSE Higher

1.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

2.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

3.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

4.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

5.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

6.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.

7.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

8.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.

9.Work out (2/3)² + (1/2)². Give your answer as a fraction.

10.Work out (−6) + (−4) × 3

11.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

13.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

14.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

15.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.